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Answer:
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval. The variance is the same as the mean.
Average rate of 56 calls per hour:
This means that , in which n is the number of hours.
Find the average and standard deviation of the number of service calls in a 15-minute period.
15 minute is one fourth of a hour, which means that . So
The variance is also 14, which means that the standard deviation is
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.